9. Anya and Sue each have $90.
Anya spends 5 over 8 of her money.
Sue spends 60% of her money.
Who has spent the most money?​

Answer:

1. x = 12

2. 3∛4 feet.

Step-by-step explanation:

1. We are given the equation of x as [tex]\sqrt{x - 3} + x = 9[/tex] and we have to find the extraneous solution of the equation.

Now, [tex]\sqrt{x - 3} + x = 9[/tex] ............. (1)

⇒ [tex]\sqrt{x - 3} = 9 - x[/tex]

Squaring both sides we get,

⇒ x - 3 = 81 - 18x + x²

⇒ x² - 19x + 84 = 0

⇒ x² - 12x - 7x + 84 = 0

⇒ (x - 12)(x - 7) = 0

⇒ x = 12 or 7.

Now, putting x = 12 in the equation (1) we get,

[tex]\sqrt{12 - 3} + 12 \neq 9[/tex]

Again, putting x = 7 in the equation (1) we get,

[tex]\sqrt{7 - 3} + 7 = 9[/tex]

Therefore, x = 12 is an extraneous solution of this equation. (Answer)

2. The volume of a cube with side lengths a ft. is given to be 108 ft³.

So, a³ = 108

⇒ a = 3∛4 feet.

Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)

Answer:

10x+20

Step-by-step explanation:

Answer: The equation is 10x+20

(x is a variable, not a multiplication symbol)

Step-by-step explanation:

10 times a number, that is unknown, plus 20.

x is the unknown number.

10x plus 20.

10x+20

The solution for (x^2+x-17) / (x-4) is (x + 5) + 3/(x-4)

Step-by-step explanation:

The given polynomial is (x^2+x-17) divided by (x-4)

Steps for long division method :

Using long division method :

        x + 5                  

x-4 |  x^2 + x - 17  

    (-)(x^2 - 4x)

                 5x - 17

              (-)(5x -20)      

                         3    

The quotient is (x+5).

The remainder is 3.

The solution is written in the form of quotient + remainder/ divisor

∴ The final answer is (x^2+x-17) / (x-4) = (x + 5) + 3/(x-4)

Final answer:

To divide (x²+x-17) by (x-4) using polynomial long division, divide the highest order term of the dividend by the highest order term of the divisor, multiply the divisor by the result, subtract the result from the dividend, and repeat until there are no more terms or the remainder has lower degree. The quotient is x+5 and the remainder is -3.

Explanation:

To divide (x²+x-17) by (x-4) using polynomial long division:

Write the dividend (x²+x-17) and the divisor (x-4) in the division format.

Divide the highest order term of the dividend (x²) by the highest order term of the divisor (x). The result is x.

Multiply the entire divisor (x-4) by the result from step 2 (x) and write the result below the dividend.

Subtract the result from step 3 from the dividend.

Repeat steps 2-4 until there are no more terms to bring down or the degree of the remainder is less than the degree of the divisor.

The final quotient is x+5 and the remainder is -3.

Answer:

42)  122.72 square inches

43) 212.83 additional feet of fabric

Step-by-step explanation:

42)

Diameter = [tex]12\frac{1}{2}[/tex] = 12.5 inches

Radius = (1/2) * Diameter = (1/2) * 12.5 = 6.25 inches

The formula for calculating the area of a circle is π * Radius²

π * Radius²

Substitute radius and pi into formula

3.14159265359 * 6.25²

Solve exponent

3.14159265359 * 39.0625

Multiply

122.7184630309

Round to the nearest hundredth

122.72 square inches

43)  Clarissa needs 500 feet of fabric

She has these pieces

3 pieces of fabric that are each 18 yards long

1 piece of fabric that is [tex]16\frac{1}{2}[/tex] yards long

1 piece of fabric that is [tex]75\frac{2}{3}[/tex] feet long

Convert all yard measurements to feet and all fractions to decimals

(1 yard = 3 feet)

3 pieces of fabric that are each 54 feet long

1 piece of fabric that is 49.5 yards long

1 piece of fabric that is 75.67 feet long

Add all lengths

3(54) + 49.5 + 75.67

162 + 49.5 + 75.67 = 287.17

Subtract from 500 to find missing length

500 - 287.17 = 212.83

212.83 additional feet of fabric

Hope this helps :)

Answer:

  x = -37 7/15

Step-by-step explanation:

1. Find the terms with the variable. They are 4.3x on the left and 4.0x on the right.

2. Identify the term with the least coefficient*. It is 4.0x on the right.

3. Subtract that term from both sides of the equation.

  4.3x -4.0x +19.35 = 8.11 +4.0x -4.0x

  0.3x +19.35 = 8.11 . . . . . . simplify

4. Identify any constant term on the side of the equation with the variable. It is 19.35 on the left.

5. Subtract that constant from both sides of the equation.

  0.3x +19.35 -19.35 = 8.11 -19.35

  0.3x = -11.24 . . . . . . . simplify

6. Divide both sides of the equation by the coefficient of the variable. That coefficient is 0.3 in this equation.

  (0.3x)/0.3 = (-11.24)/0.3

  x = -37.466666... (repeating decimal)

__

If you like, you can express the solution as a mixed number:

  x = -11.24/0.30 = -1124/30 = -562/15

  x = -37 7/15

_____

You are expected to be able to do the math using the numbers in any form they might appear: integers, mixed numbers, fractions, decimals, scientific notation. You can convert the problem here to an integer problem by multiplying both sides by 100:

  430x +1935 = 811 +400x

The answer still has a fraction in it: x= -1124/30 = -37 7/15.

_____

* You subtract the term with the least coefficient so the variable term in the result has a positive coefficient. That may be desirable, but is not necessary. You can subtract either variable term to get the variable on one side of the equal sign. You have to pay attention to the resulting sign when you divide by the variable's coefficient.

Square of m reduced by 49 = m²- 49

Step-by-step explanation:

Let us consider the variable as m.

Square of m is given as m².

Reduction factor is 49.

So the expression for the square of m reduced by 49 is given as m²- 49.

Answer: 1,360

Step-by-step explanation:

20 * 20 = 400

20 * 12 = 240

240 * 4 = 960

960 + 400 = 1,360

Answer:

1/6

Step-by-step explanation:

Answer:

[tex]b+g=26[/tex]

[tex]b=g-3[/tex]

Step-by-step explanation:

Let the number of boys be reprented by [tex]b[/tex]

Let the number of girls be represented by [tex]g\\[/tex]

↓ Total number of boys + girls must be 26

[tex]b+g=26[/tex]

↓ Number of boys is 3 less than the number of girls

[tex]b=g-3[/tex]

The system of equations that represents the number of boys and girls are [tex]x+y=26[/tex] and [tex]x = y-3[/tex] and this can be determined by forming the linear equation.

Given :

The following steps can be used in order to determine the system of equations that represents the number of boys and girls:

Step 1 - Let the total number of boys be 'x' and the total number of girls be 'y'.

Step 2 - So, the linear equation that represents the total number of students in Mrs. Augello's math class is:

[tex]x+y=26[/tex]    --- (1)

Step 3 - The linear equation that represents the situation "number of boys is three less than the number of girls" is:

[tex]x = y-3[/tex]   --- (2)

For more information, refer to the link given below:

https://brainly.com/question/11897796

[tex]\( f(2) = \ln \left( \frac{14}{3} \right) \)[/tex]. You can calculate this value to get a numerical result.

To find the particular solution [tex]\( y = f(x) \)[/tex] to the given differential equation [tex]\( \frac{dy}{dx} = \frac{x^2 + 1}{e^y} \)[/tex] with the initial condition [tex]\( f(1) = 0 \)[/tex] and then evaluate [tex]\( f(2) \),[/tex] we can follow these steps:

1. Separate variables:

[tex]\[ e^y dy = (x^2 + 1) dx \][/tex]

2. Integrate both sides:

[tex]\[ \int e^y dy = \int (x^2 + 1) dx \][/tex]

[tex]\[ e^y = \frac{1}{3} x^3 + x + C \][/tex]

3. Apply the initial condition [tex]\( f(1) = 0 \):[/tex]

[tex]\[ e^0 = \frac{1}{3} (1)^3 + 1 + C \][/tex]

[tex]\[ 1 = \frac{1}{3} + 1 + C \][/tex]

[tex]\[ C = \frac{2}{3} \][/tex]

So, the particular solution is:

[tex]\[ e^y = \frac{1}{3} x^3 + x + \frac{2}{3} \][/tex]

4. Solve for  y :

[tex]\[ y = \ln \left( \frac{1}{3} x^3 + x + \frac{2}{3} \right) \][/tex]

Now, we need to find f(2), which means finding the value of y when  x = 2:

[tex]\[ y = \ln \left( \frac{1}{3} (2)^3 + 2 + \frac{2}{3} \right) \][/tex]

[tex]\[ y = \ln \left( \frac{8}{3} + 2 + \frac{2}{3} \right) \][/tex]

[tex]\[ y = \ln \left( \frac{14}{3} \right) \][/tex]

Answer:

The amount of stock for which both brokers would charge the same commission is $2500.

Step-by-step explanation:

i) Let the amount of stock to be traded be worth $x

ii) therefore for both the brokers to charge the same commission we can write

   1% of x  = $25 [tex]\RIghtarrow[/tex][tex]\Rightarrow[/tex]  0.01 [tex]\times[/tex] x  = 25  [tex]\therefore[/tex]   x = [tex]\frac{25}{0.01} = 2500[/tex]

The amount of stock for which both brokers would charge the same commission is $2500.

Answer:

[tex]11\frac{3}{8}\ yd[/tex]

Step-by-step explanation:

we know that

To find out the total yards of fabric used, add up the yards of fabric used for Nickys' room and the yards of fabric used for Linda's room

so

[tex]4\frac{3}{4}+6\frac{5}{8}[/tex]

Convert mixed number to an improper fraction

[tex]4\frac{3}{4}\ yd=4+\frac{3}{4}=\frac{4*4+3}{4}=\frac{19}{4}\ yd[/tex]

[tex]6\frac{5}{8}\ yd=6+\frac{5}{8}=\frac{6*8+5}{8}=\frac{53}{8}\ yd[/tex]

Adds the fractions

[tex]\frac{19}{4}+\frac{53}{8}=\frac{2*19+53}{8}= \frac{91}{8}\ yd[/tex]

Convert to mixed number

[tex]\frac{91}{8}\ yd= \frac{88}{8}+ \frac{3}{8}= 11\frac{3}{8}\ yd[/tex]

-1/2x < -12

Divide both sides by -1/2

Also because you are dividing by a negative number you need to reverse the inequality sign.

X > 24

Answer:

lool at the picture shown

To evaluate the expression[tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) for \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\),[/tex]let's substitute these values into the expression:

[tex]\[3\left(\frac{2}{3}\right)^3 - \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 + \frac{2}{3} \times \frac{1}{2}\][/tex]

Let's simplify this step by step.

1. [tex]\(3\left(\frac{2}{3}\right)^3 = 3 \times \frac{8}{27} = \frac{24}{27} = \frac{8}{9}\)[/tex]

2.  [tex]\(- \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 = - 2 \times 2^6 \times \frac{1}{3^2} \times \frac{1}{2^2} = - 2 \times 64 \times \frac{1}{9} \times \frac{1}{4} = - \frac{128}{9}\)[/tex]

3   .[tex]\(\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}\)[/tex]

Now, let's add these results together:

[tex]\[\frac{8}{9} - \frac{128}{9} + \frac{1}{3} = \frac{8 - 128 + 3}{9} = \frac{-117}{9} = -\frac{13}{3}\][/tex]

So, [tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) evaluated at \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\) is \(-\frac{13}{3}\).[/tex]

Answer:

The answer is (-2,0)

Step-by-step explanation:

When you put both points on the graph. Draw a line through them.

See where the line hits a point from in between the points.

Final answer:

By setting up an equation based on the given information that Jim is 2 years older than 3 times Tommy's age and their combined ages are 18, we find that Tommy is 4 years old and Jim is 14 years old.

Explanation:

The question is about finding the ages of Jim and his younger brother Tommy given that Jim is 2 years older than 3 times Tommy's age and together their ages add up to 18. Let's denote Tommy's age as T years. Therefore, Jim's age would be 3T + 2 years. According to the problem, if we add both ages, the sum is 18. So, we can set up the following equation to find their ages:

T + (3T + 2) = 18

Simplifying this equation gives:

4T + 2 = 18

4T = 16

T = 4

Thus, Tommy is 4 years old. To find Jim's age, we substitute Tommy's age back into the equation for Jim's age:

Jim's age = 3(4) + 2 = 12 + 2 = 14

Therefore, Tommy is 4 years old, and Jim is 14 years old.

Answer:Therefore the two numbers are -20 and -40

Step-by-step explanation:

Let the two numbers be a and b,

It is given that their sum is 60, so a + b = -60,

It is also given that their difference is 20, so a - b = 20,

Since we don’t know yet which one out of a and b is greater, assume any one of them to be larger than the other (a in my case),

Add the above two equations, you get,

2a = -40 or a = -20,

Substitute this value of a in any of the formed equations,

a + b = -60,

-20 + b = -60 or b = -40,

Let the two numbers be a and b,

It is given that their sum is 60, so a + b = -60,

It is also given that their difference is 20, so a - b = 20,

Since we don’t know yet which one out of a and b is greater, assume any one of them to be larger than the other (a in my case),

Add the above two equations, you get,

2a = -40 or a = -20,

Substitute this value of a in any of the formed equations,

a + b = -60,

-20 + b = -60 or b = -40,

Therefore the two numbers are -20 and -40

The smaller number is 17, and the larger number is 43. The two equations formed from the given information are solved simultaneously to find these numbers.

To solve this problem, we need to set up two equations based on the given information. Let's denote the smaller number by s and the larger number by l.

The sum of the two numbers is 60: s + l = 60.

If twice the smaller number is subtracted from the large number, the result is 9: l - 2s = 9.

We can solve these equations simultaneously. First, rearrange the second equation to express l in terms of s: l = 2s + 9. Next, substitute this expression into the first equation:

s + (2s + 9) = 60

3s + 9 = 60

3s = 51

s = 17

Now we have found the smaller number is 17. To find the larger number, we substitute s back into the equation for l:

l = 2(17) + 9

l = 34 + 9

l = 43

So the two numbers are 17 and 43

Answer:

(2004+2005) divided by 2

Step-by-step explanation:

Answer:

the graph of the equation will  be symmetric about option b.) x axis

Step-by-step explanation:

i) the given equation is x = [tex]y^2[/tex] + 4

ii) therefore [tex]y^{2}[/tex] = x - 4

iii) the equation is that of a parabola with vertex at (4,0)

iv) the graph of the equation will  be symmetric about option b.) x axis

Answer:

55

Step-by-step explanation:

The two shortest sides added up need to be longer then the longest angle so 48 + 55 = 103>73

The function rule that relates y (circumference) to x (diameter) is y = π x [pi × x]

Since x represents the diameter of the circle and y represents the circumference.

For a circle with radius r, circumference of the circle (y)equals,

y = 2πr ................................(1)

Diameter of a circle is twice the radius of the circle.

Assuming x as the diameter

[tex]x = 2\times r = 2r[/tex] ...........................(2)

Substituting (2) in (1), we get

y = π(2r) = πx ..............................................(3)

A function rule is an equation that determines the relation between a dependent variable and an independent variable. The relation between diameter of a circle and its circumference can be given as

Circumference = Pi × Diameter of circle

y = π × x

where π = 3.142

[tex](-1, 9), \ (0, 6), \ (1, 4), \ (2, 2\frac{2}{3} ), \ (1, \frac{7}{9} )[/tex]

Solution:

Given [tex]f(x)=6\left(\frac{2}{3}\right)^{x}[/tex]

Domain = {–1, 0, 1, 2, 3}

Substitute the given values in the function.

At x = –1,

[tex]f(-1)=6\left(\frac{2}{3}\right)^{-1}[/tex]

         [tex]=6 \times \frac{3}{2}[/tex]

         = 9

[tex](x, f(x))=(-1, 9)[/tex]

At x = –0,

[tex]f(0)=6\left(\frac{2}{3}\right)^{0}=6[/tex]

[tex](x, f(x))=(0,6)[/tex]

At x = 1,

[tex]f(1)=6\left(\frac{2}{3}\right)^{1}=4[/tex]

[tex](x, f(x))=(1,4)[/tex]

At x = 2,

[tex]f(2)=6\left(\frac{2}{3}\right)^{2}[/tex]

       [tex]=\frac{24}{9}[/tex]

      [tex]=2\frac{6}{9}[/tex] (Cancel the common terms)

      [tex]=2\frac{2}{3}[/tex]

[tex](x, f(x))=(2, 2\frac{2}{3} )[/tex]

At x = 3,

[tex]f(3)=6\left(\frac{2}{3}\right)^{3}[/tex]

       [tex]=\frac{48}{27}[/tex] (Cancel the common terms)

       [tex]=\frac{16}{9}[/tex]

      [tex]=1\frac{7}{9}[/tex]

[tex](x, f(x))=(3, 1\frac{7}{9} )[/tex]

Plot the points in the graph.

The image of the graph is attached below.

Answer: 26

Step-by-step explanation: I think so...

Answer:

26

Step-by-step explanation:

Answer:

Patty spent $71.75

Step-by-step explanation:

20.50 x 3.5 = 71.75

Answer: 71.75

3.5* 20.50

Answer:

SinB = Sin30 = 0.5

Step-by-step explanation:

Ok lets use sine rule

a/SinA = b/SinB = c/SinC

a/Sin60 = b/SinB = 12/Sin90

b/Sin30 = 12/Sin90

b = (12 × Sin30) ÷ Sin90

b = (12 × 0.5) ÷ 1

b = 6cm

SinB = Sin30 = 0.5

Answer:45

Step-by-step explanation:

it is 45

Step-by-step explanation:

I will have "x" represent the unknown number, or you could use a "?", doesn't matter.

[tex]8\leq \frac{x}{-4}[/tex]     [8 is less than or equal to (≤) the quotient (÷) of a number and -4, so the number is being divided by -4]

If you need to solve this, you need to isolate/get the variable "x" by itself in the inequality:

[tex]8\leq \frac{x}{-4}[/tex]   Multiply -4 on both sides to get rid of the fraction and get "x" by itself

[tex](-4)8\geq \frac{x}{-4} (-4)[/tex]    When you multiply/divide by a negative number, you flip the sign (< >)

-32 ≥ x          [-32 is greater than or equal to x, or x is less than or equal to -32]